What is the trigonometric form of # (-4+3i) #?

Question

2666 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-18T14:30:08

#5costheta+i5sintheta#, where #theta=tan^(-1)(-3/4)#

Trigonometric form of a complex number #a+bi# is #rcostheta+isintheta#.

As such here, #rcostheta=-4# and #rsintheta=3#.

Squaring the two and adding

#r^2(cos^2theta+sin^2theta)=(-4)^2+3^2=16+9=25#

or #r^2=25# and #r=5#

Dividing we get #(rsintheta)/(rcostheta)=#-3/4# or

#tantheta=-3/4# or #theta=tan^(-1)(-3/4)#

Hence #a+bi# in trigonometric form is #5costheta+i5sintheta#, where #theta=tan^(-1)(-3/4)#